What is the limit as t approaches 1 of (t-1)/(t^3-1) ?

The limit as t approaches 1 of (t-1)/(t^3-1) is 1/3

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limit as t approaches 1 of (t-1)/(t^3-1)

t \to 1 lim (\frac{t - 1}{t ^{3} - 1})

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

t \to 1 lim (\frac{t - 1}{t ^{3} - 1})

Simplify

\frac{t - 1}{t ^{3} - 1} : \frac{1}{t ^{2} + t + 1}

= t \to 1 lim (\frac{1}{t ^{2} + t + 1})

Plug in the value

t = 1

= \frac{1}{1 ^{2} + 1 + 1}

Simplify

= \frac{1}{3}

What is the limit as t approaches 1 of (t-1)/(t^3-1) ?
The limit as t approaches 1 of (t-1)/(t^3-1) is 1/3